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Item Bayesian Optimization of Active Materials for Lithium-Ion Batteries(SAE, 2021-04) Valladares, Homero; Li, Tianyi; Zhu, Likun; El-Mounayri, Hazim; Tovar, Andres; Hashem, Ahmed; Abdel-Ghany, Ashraf E.; Mechanical Engineering, School of Engineering and TechnologyThe design of better active materials for lithium-ion batteries (LIBs) is crucial to satisfy the increasing demand of high performance batteries for portable electronics and electric vehicles. Currently, the development of new active materials is driven by physical experimentation and the designer’s intuition and expertise. During the development process, the designer interprets the experimental data to decide the next composition of the active material to be tested. After several trial-and-error iterations of data analysis and testing, promising active materials are discovered but after long development times (months or even years) and the evaluation of a large number of experiments. Bayesian global optimization (BGO) is an appealing alternative for the design of active materials for LIBs. BGO is a gradient-free optimization methodology to solve design problems that involve expensive black-box functions. An example of a black-box function is the prediction of the cycle life of LIBs. The cycle life cannot be predicted using a simple closed-form expression but only through the cycling performance test or a numerical simulation. BGO has two main components: a surrogate probabilistic model of the black-box function and an acquisition function that guides the optimization. This research employs BGO in the design of cathode active materials for LIB cells. The training data corresponds to the initial capacity and cycle life of five coin cells with different compositions of LiNixMn2 − xO4 in their cathode, where x is the content of Ni. BGO utilizes the experimental data to identify five new compositions that can produce cells with high initial capacity and\or large cycle life. The surrogate models of the initial capacity and cycle life are Gaussian Processes. The acquisition function is the constrained multi-objective expected improvement. The results show that BGO can identify high-performance active materials for LIBs. Designers can use the data generated during the optimization to decide the composition of the next batch of active materials to be tested, i.e., guide the physical experimentation.Item Gaussian process-based prognostics of lithium-ion batteries and design optimization of cathode active materials(Elsevier, 2022-04-30) Valladares, Homero; Li , Tianyi; Zhu, Likun; El-Mounayri, Hazim; Hashem, Ahmed M.; Abdel-Ghany, Ashraf E.; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and TechnologyThe increasing adoption of lithium-ion batteries (LIBs) in consumer electronics, electric vehicles, and smart grids poses two challenges: the accurate prediction of the battery health to prevent operational impairments and the development of new materials for high-performance LIBs. Characterized by their flexibility and mathematical tractability, Gaussian processes (GPs) provide a powerful framework for monitoring and optimization tasks. This study employs two GP-based techniques: co-kriging surrogate modelling and Bayesian optimization. The GP training data comes from the cycling performance test of five CR2032 cells with Ni contents of 0.0, 0.4, 0.5, 0.6, and 1.0 in their cathode active material Li2NixMn2-xO4. The co-kriging surrogate predicts the capacity degradation profile of a cell by exploiting information from different cells. Bayesian optimization identifies new Ni compositions that can produce cells with high initial specific capacity and large cycle life. The study shows the predictive capabilities of the co-kriging surrogate when correlated data is available. Bayesian optimization predicts that a Ni content of 0.44 produces cells with an initial specific capacity of 103.4 ± 3.8 mAh g−1 and a cycle life of 595 ± 12 cycles. Furthermore, the Bayesian strategy identifies other Ni contents that can improve the overall quality of the current Pareto front.Item Multi-Objective Bayesian Optimization of Lithium-Ion Battery Cells for Electric Vehicle Operational Scenarios(MDPI AG, 2022-05-31) Gaonkar, Ashwin; Valladares, Homero; Tovar, Andres; Zhu, Likun; El-Mounayri , Hazim; Mechanical Engineering, School of Engineering and TechnologyThe development of lithium-ion batteries (LIBs) based on current practice allows an energy density increase estimated at 10% per year. However, the required power for portable electronic devices is predicted to increase at a much faster rate, namely 20% per year. Similarly, the global electric vehicle battery capacity is expected to increase from around 170 GWh per year today to 1.5 TWh per year in 2030—this is an increase of 125% per year. Without a breakthrough in battery design technology, it will be difficult to keep up with their increasing energy demand. The objective of this investigation is to develop a design methodology to accelerate the LIB development through the integration of electro-chemical numerical simulations and machine learning algorithms. In this work, the Gaussian process (GP) regression model is used as a fast approximation of numerical simulation (conducted using Simcenter Battery Design Studio®). The GP regression models are systematically updated through a multi-objective Bayesian optimization algorithm, which enables the exploration of innovative designs as well as the determination of optimal configurations. The results reported in this work include optimal thickness and porosities of LIB electrodes for several practical charge–discharge scenarios which maximize energy density and minimize capacity fade.Item Multi-Objective Bayesian Optimization of Lithium-Ion Battery Cells for Electric Vehicle Operational Scenarios(MDPI, 2022-05-31) Gaonkar, Ashwin; Valladares, Homero; Tovar, Andres; Zhu, Likun; El-Mounayri, Hazim; Mechanical and Energy Engineering, School of Engineering and TechnologyThe development of lithium-ion batteries (LIBs) based on current practice allows an energy density increase estimated at 10% per year. However, the required power for portable electronic devices is predicted to increase at a much faster rate, namely 20% per year. Similarly, the global electric vehicle battery capacity is expected to increase from around 170 GWh per year today to 1.5 TWh per year in 2030—this is an increase of 125% per year. Without a breakthrough in battery design technology, it will be difficult to keep up with their increasing energy demand. The objective of this investigation is to develop a design methodology to accelerate the LIB development through the integration of electro-chemical numerical simulations and machine learning algorithms. In this work, the Gaussian process (GP) regression model is used as a fast approximation of numerical simulation (conducted using Simcenter Battery Design Studio®). The GP regression models are systematically updated through a multi-objective Bayesian optimization algorithm, which enables the exploration of innovative designs as well as the determination of optimal configurations. The results reported in this work include optimal thickness and porosities of LIB electrodes for several practical charge–discharge scenarios which maximize energy density and minimize capacity fade.Item Multi-Objective Bayesian Optimization Supported by Gaussian Process Classifiers and Conditional Probabilities(ASME, 2022-11-11) Valladares, Homero; Tovar, Andres; Mechanical Engineering, School of Engineering and TechnologyIn the last years, there has been an increasing effort to develop Bayesian methodologies to solve multi-objective optimization problems. Most of these methods can be classified in two groups: infilling criterion-based methods and aggregation-based methods. The first group employs an index that quantifies the gain that a new design can produce in the current Pareto front while the last group uses a (possibly non-linear) aggregation function and a weighting vector to identify a Pareto design. Most infilling-based methods have been developed to solve two-objective optimization problems. Aggregation-based methods enable the solution of many-objective optimization problems but their performance depends on the set of weighting vectors, which are often selected randomly. This study proposes a novel multi-objective Bayesian framework that exploits the rich probabilistic information that can be extracted from Gaussian process (GP) classifiers and the ability of conditional probabilities to capture design preferences. In the proposed framework, a GP classifier is trained to identify design zones that potentially contain Pareto designs. The training process involves the inference of a latent GP that encodes input-space interactions that describe a Pareto design. This latent GP enables the solution of many-objective optimization problems with any standard acquisition function and without the prescription of a weighting vector. Conditional probabilities are utilized to define design goals that promote a uniform expansion of the Pareto front. The proposed approach is demonstrated with two benchmark analytical problems and the design optimization of sandwich composite armors for blast mitigation, which involves expensive finite element simulations.Item Multilevel Design of Sandwich Composite Armors for Blast Mitigation using Bayesian Optimization and Non-Uniform Rational B-Splines(2021) Valladares, Homero; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and TechnologyIn regions at war, the increasing use of improvised explosive devices (IEDs) is the main threat against military vehicles. Large cabin”s penetrations and high gross accelerations are primary threats against the occupants” survivability. The occupants” survivability under an IED event largely depends on the design of the vehicle armor. Under a blast load, a vehicle armor should maintain its structural integrity while providing low cabin penetrations and low gross accelerations. This investigation employs Bayesian global optimization (BGO) and non-uniform rational B-splines (NURBS) to design sandwich composite armors that simultaneously mitigate the cabin”s penetrations and the reaction force at the armor”s supports. The armors are made of four layers: steel, carbon fiber reinforced polymer (CFRP), aluminum honeycomb, and CFRP. BGO is a methodology to solve optimization problems that require the evaluation of expensive black-box functions such as the finite element (FE) simulations of the vehicle armor under a blast event. BGO has two main components: the surrogate model of the black-box function and the acquisition function that guides the optimization. In this study, the surrogate models are Gaussian processes and the acquisition function is the multi-objective expected improvement function. NURBS generate the armor”s shape. The numerical examples show three alternatives to optimize the armor at two levels: (1) thicknesses of the sandwich”s layers and (2) the armor”s shape. The three design alternatives differ in the number of optimized levels and the optimization approach (sequential or simultaneous). The results show that the simultaneous optimization of the thicknesses of the sandwich”s layers and the armor”s shape is the most effective approach to design vehicle armors for blast mitigation.Item Multiscale Topology Optimization With Gaussian Process Regression Models(American Society of Mechanical Engineers, 2021-08-17) Najmon, Joel C.; Valladares, Homero; Tovar, Andres; Mechanical Engineering, School of Engineering and TechnologyMultiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.Item Nonlinear Multi-Fidelity Bayesian Optimization: An Application in the Design of Blast Mitigating Structures(SAE International, 2022-03-29) Valladares, Homero; Tovar, Andres; Mechanical Engineering, School of Engineering and TechnologyA common scenario in engineering design is the availability of several black-box functions that describe an event with different levels of accuracy and evaluation cost. Solely employing the highest fidelity, often the most expensive, black-box function leads to lengthy and costly design cycles. Multi-fidelity modeling improves the efficiency of the design cycle by combining information from a small set of observations of the high-fidelity function and large sets of observations of the low-fidelity, fast-to-evaluate functions. In the context of Bayesian optimization, the most popular multi-fidelity model is the auto-regressive (AR) model, also known as the co-kriging surrogate. The main building block of the AR model is a weighted sum of two Gaussian processes (GPs). Therefore, the AR model is well suited to exploit information generated by sources that present strong linear correlations. Recently, the non-linear auto-regressive Gaussian process (NARGP) model has appeared as an alternative to integrate information generated by non-linearly correlated black-box functions. The performance of the NARGP model in structural optimization has remained largely unexplored. This investigation presents a Bayesian optimization approach that implements the NARGP model as the multi-fidelity surrogate model. The optimization strategy is utilized in the design sandwich composite armors for blast mitigation. The armors are made of four layers: steel, carbon fiber reinforced polymer (CFRP), aluminum honeycomb (HC), and CFRP. The optimization problem has three design variables, which are the thickness of the CFRP and aluminum HC layers. Two objectives are minimized: the armor’s penetrations and the reaction force at the armor’s supports. The black-box functions are two finite element models with different levels of fidelity. The low-fidelity model assumes elastic behavior of the sandwich composite. The high-fidelity model considers the nonlinear behavior of each layer of the armor. The results show that the proposed non-linear multi-fidelity Bayesian optimization approach produces a more stable expansion of the Pareto front than an optimization strategy that employs the AR model. This outcome suggests that the NARGP model is an appealing alternative in design problems with a limited number of function evaluations of the high-fidelity source.Item Optimization of Chessboard Scanning Strategy Using Genetic Algorithm in Multi-Laser Additive Manufacturing Process(ASME, 2021-02) Malekipour, Ehsan; Valladares, Homero; Shin, Yung; El-Mounayri, Hazim; Mechanical and Energy Engineering, School of Engineering and TechnologyResidual stress and manufacturing time are two serious challenges that hinder the widespread industry adoption and implementation of the powder-bed fusion (PBF) process. Commercial Multi-Laser PBF (ML-PBF) systems have been developed by several vendors in recent years, which dramatically increase the production rate by employing more heat sources (up to 4 laser beams). Although numerous research works conducted toward mitigation of the effects of residual stress on printed parts in the Single Laser PBF (SL-PBF) process, no research work on this topic has been reported for the ML-PBF process to date. One of the most efficient real-time approaches to mitigate the influence of residual stress and as such the process lead time effectively is to improve the scanning strategy. This approach can be also implemented effectively in the ML-PBF process. In this work, we extend the previously developed GAMP (Genetic Algorithm Maximum Path) strategy for optimizing the scanning path in ML-PBF. The E-GAMP (the Extended GAMP) strategy manipulates the printing topology of the islands and generates more thermally efficient scanning patterns for the chessboard scanning strategy in ML-PBF. This strategy extends the single thermal heat source to multiple ones (2 as well as 3 lasers). To validate the effectiveness of the proposed strategy, we simulate the thermal distribution throughout a simple rectangular layer by ABAQUS for both the traditional successive scanning strategy and the E-GAMP strategy. The results demonstrate that the E-GAMP strategy considerably decreases the manufacturing time while it reduces the maximum temperature gradient, or in other words, generates a more uniform temperature distribution throughout the exposure layer.Item Structural Optimization of Thin-Walled Tubular Structures for Progressive Collapse Using Hybrid Cellular Automaton with a Prescribed Response Field(SAE, 2019) Valladares, Homero; Najmon, Joel; Tovar, Andres; Mechanical and Energy Engineering, School of Engineering and TechnologyThe design optimization of thin-walled tubular structures is of relevance in the automotive industry due to their low cost, ease of manufacturing and installation, and high-energy absorption efficiency. This study presents a methodology to design thin-walled tubular structures for crashworthiness applications. During an impact, thin-walled tubular structures may exhibit progressive collapse/buckling, global collapse/buckling, or mixed collapse/buckling. From a crashworthiness standpoint, the most desirable collapse mode is progressive collapse due to its high-energy absorption efficiency, stable deformation, and low peak crush force (PCF). In the automotive industry, thin-walled components have complex structural geometries. These complexities and the several loading conditions present in a crash reduce the possibility of progressive collapse. The Hybrid Cellular Automata (HCA) method has shown to be an efficient continuum-based approach in crashworthiness design. All the current implementations of the HCA method use a scalar set point to design structures with a uniform distribution of a field variable, e.g., stress, strain, internal energy density (IED), mutual potential energy. For example, using IED and mutual potential energy as the field variable result in high stiffness and progressive collapsing structures, respectively. This paper presents a modified version of the HCA method to design thin-walled structures that collapse progressively. In this methodology, the set point has two components, a prescribed response field, which promotes progressive collapse, and a variable offset value, which satisfies the mass constraint. The numerical examples show that this modified HCA method is capable of finding material distributions that exhibit progressive collapse, resulting in significant improvement in specific energy absorption (SEA) with relatively little change in the PCF.